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A008013 Coordination sequence occurring in Zeolite Codes AFG, CAN, LIO, LOS.

%I A008013 #37 Feb 07 2024 09:00:06
%S A008013 1,4,10,20,34,54,78,104,134,168,210,256,302,352,406,470,538,604,674,
%T A008013 748,834,924,1010,1100,1194,1302,1414,1520,1630,1744,1874,2008,2134,
%U A008013 2264,2398,2550,2706,2852,3002,3156,3330,3508,3674,3844,4018,4214,4414,4600
%N A008013 Coordination sequence occurring in Zeolite Codes AFG, CAN, LIO, LOS.
%D A008013 W. M. Meier, D. H. Olson, and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.
%H A008013 Vincenzo Librandi, <a href="/A008013/b008013.txt">Table of n, a(n) for n = 0..1000</a>
%H A008013 R. W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Coordination Sequences and Encyclopedia of Integer Sequences</a>.
%H A008013 R. W. Grosse-Kunstleve, G. O. Brunner, and N. J. A. Sloane, <a href="http://neilsloane.com/doc/ac96cs/">Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites</a>, Acta Cryst., A52 (1996), pp. 879-889.
%H A008013 Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>.
%H A008013 International Zeolite Association, <a href="http://www.iza-structure.org/databases/">Database of Zeolite Structures</a>.
%H A008013 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,2,-2,0,0,0,-1,1).
%F A008013 a(5m)=52*m^2+2, a(5m+1)=52*m^2+22*m+4, a(5m+2)=52*m^2+42*m+10, a(5m+3)=52*m^2+62*m+20, a(5m+4)=52*m^2+82*m+34. - _N. J. A. Sloane_
%F A008013 G.f.: -(x+1)^3*(x^8+3*x^6+5*x^4+3*x^2+1) / ((x-1)^3*(x^4+x^3+x^2+x+1)^2). - _Colin Barker_, Dec 12 2012
%t A008013 CoefficientList[Series[-(x + 1)^3 (x^8 + 3 x^6 + 5 x^4 + 3 x^2 + 1)/((x - 1)^3 (x^4 + x^3 + x^2 + x + 1)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%K A008013 nonn,easy
%O A008013 0,2
%A A008013 _Ralf W. Grosse-Kunstleve_